# The lexicographic equal-loss solution

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- [S.l.] : Elsevier Science
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PII: 0165-4896(91)90004-B Mathematical Social Sciences 22 (1991) 151-161 North-Holland 151 The lexicographic equal-loss solution Youngsub Chun Deparrmenr of Economics, Seoul National University, Seoul 151.742, Korea Hans Peters Deparimeni of Mathematics, University of Limburg, P.O. Box 6I6, 6200 MD Maastricht, Netherlands Communicated by H. Moulin Received 7 April i989 Revised 17 June 1991 We introduce a new solution for Nash’s bargaining problem, called the lexicographic equal-loss solu- tion. This solution is a lexicographic extension of the equal-loss solution, which equalizes across agents the losses from the ideal point, to satisfy Pareto optimality. An axiomatic characterization is presented by using the following five axioms: Pareto optimality, anonymity, translation invariance, weak monotonicity, and independence of alternatives other than the ideal point. Key words: Bargaining problem; lexicographic equal-loss solution; axiomatic characterization. 1. Introduction Suppose a bundle of goods is to be divided or redivided between a number of agents. Among the many criteria according to which such a division might be chosen, consider the following pair of more or less complementary criteria: either the utility gains of agents relative to their utility levels of initial holdings are impor- tant, or their utility losses with respect to their maximally attainable utilities. One appropriate framework for studying problems like the division problem above, is axiomatic bargaining theory, which started with the seminal paper by Nash (1950).’ Solutions can be judged according to the gains or losses criteria. Typical examples of solutions for which the gains criterion is central, are the egalitarian and lexicographic egalitarian solutions (for formal definitions of these solutions, see the next section); for which either the gains or the losses criterion can be relevant-the Kalai-Smorodinsky (1975) solution. In this pa

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